### Table 1. Computational costs for the Bellare-Neven IBMS scheme, the Gentry-Ramzan IBMS scheme and our multi-key IBS (one-level) scheme. Here, ADD denotes the num- ber of elliptic curve point additions, eMUL the number of elliptic curve point multi- plications, PAI the number of pairing computations, HASH the number of hash opera- tions, mMUL the number of modular multiplications, and EXP the number of modular exponentiations.

"... In PAGE 15: ... The computational costs for these schemes are shown in Table 1. From Table1 , it is evident that our multi-key IBS scheme is much more efficient than both the Bellare-Neven and the Gentry-Ramzan IBMS schemes in terms of signing cost at an equivalent security level. Suppose our scheme and the Gentry-Ramzan IBMS scheme are instantiated using pairings defined on an elliptic curve at the 80-bit security level, while the Bellare-Neven scheme is instantiated using a 1024-bit RSA modulus (also offering roughly 80 bits of security).... ..."

### Table 8: Bucket sorting methods: impact on running time (milliseconds) of di erent algorithms for sorting buckets, in array-based burstsort.

2003

"... In PAGE 8: ... MBM radixsort and multi- key quicksort were signi cantly more e cient than the others for all data sets. The timings are reported in Table8 . In contrast to MBM radixsort, multikey quicksort is not a stable sorting algorithm.... ..."

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### Table 4. Performance Comparison of Additive Homomorphic Cryptosystems

2006

"... In PAGE 11: ...Table 4. Performance Comparison of Additive Homomorphic Cryptosystems Table4 shows the comparison of the three homomorphic cryptosystems. The size of ciphertexts reflects both the overhead of storage at the server and transmission of aggregate values.... In PAGE 12: ... The size of these tables directly affect the efficiency of the search in that the larger the tables the faster the search. When deriving the results in Table4 , we assumed aggregation of 10,000 20-bit bit values (e.g.... ..."

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### Table III. Additively Homomorphic Encryption Scheme

### Table I Five graph homomorphisms and their properties

### Table 1. Some de nitions of relational homomorphisms

### TABLE I HOMOMORPHIC HASHING FUNCTION PARAMETERS

### Table 7: Authenticator Contents Level Authenticator

1994

"... In PAGE 8: ...V.C.1. Authenticator An authenticator placed in the authenticator field in the IP option has different meanings for each security level. Table7 shows contents of authenticator for each security level. Box with 14 denotes information used to generate the authenticator.... ..."

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